1 (**************************************************************************)
4 (* ||A|| A project by Andrea Asperti *)
6 (* ||I|| Developers: *)
7 (* ||T|| The HELM team. *)
8 (* ||A|| http://helm.cs.unibo.it *)
10 (* \ / This file is distributed under the terms of the *)
11 (* v GNU General Public License Version 2 *)
13 (**************************************************************************)
15 (* This file was automatically generated: do not edit *********************)
19 (*#***********************************************************************)
21 (* v * The Coq Proof Assistant / The Coq Development Team *)
23 (* <O___,, * CNRS-Ecole Polytechnique-INRIA Futurs-Universite Paris Sud *)
25 (* \VV/ **************************************************************)
27 (* // * This file is distributed under the terms of the *)
29 (* * GNU Lesser General Public License Version 2.1 *)
31 (*#***********************************************************************)
33 (*i $Id: Zmin.v,v 1.3.2.1 2004/07/16 19:31:21 herbelin Exp $ i*)
35 (*#* Binary Integers (Pierre Cr\233\gut (CNET, Lannion, France) *)
37 include "Arith/Arith.ma".
39 include "ZArith/BinInt.ma".
41 include "ZArith/Zcompare.ma".
43 include "ZArith/Zorder.ma".
46 Open Local Scope Z_scope.
49 (*#*********************************************************************)
51 (*#* Minimum on binary integer numbers *)
53 inline procedural "cic:/Coq/ZArith/Zmin/Zmin.con" as definition.
55 (*#* Properties of minimum on binary integer numbers *)
57 inline procedural "cic:/Coq/ZArith/Zmin/Zmin_SS.con" as lemma.
59 inline procedural "cic:/Coq/ZArith/Zmin/Zle_min_l.con" as lemma.
61 inline procedural "cic:/Coq/ZArith/Zmin/Zle_min_r.con" as lemma.
63 inline procedural "cic:/Coq/ZArith/Zmin/Zmin_case.con" as lemma.
65 inline procedural "cic:/Coq/ZArith/Zmin/Zmin_or.con" as lemma.
67 inline procedural "cic:/Coq/ZArith/Zmin/Zmin_n_n.con" as lemma.
69 inline procedural "cic:/Coq/ZArith/Zmin/Zmin_plus.con" as lemma.
71 (*#*********************************************************************)
73 (*#* Maximum of two binary integer numbers *)
75 inline procedural "cic:/Coq/ZArith/Zmin/Zmax.con" as definition.
77 (*#* Properties of maximum on binary integer numbers *)
81 generalize (refl_equal name); pattern name at -1 in |- *; case name.
84 inline procedural "cic:/Coq/ZArith/Zmin/Zmax1.con" as theorem.
86 inline procedural "cic:/Coq/ZArith/Zmin/Zmax2.con" as theorem.